Can someone help with these questions:

The power series 1+atat.= (1) has interval of convergence Note: the Maple syntax for the interval [-2, 2) is [-2, 2) . If we differentiate both sides of (1), we get 1+ 2x + 3x + .= (k +1)ak If we differentiate once again, we get OO 2+2 x 3x + 3 x 4x + .. = ( k +1) x ( k + 2)ack = k=0 Dividing the last series by two gives 1 + 3x + 6x + 10x3+ ...= ( k + 1) x (k + 2)- 2 The coefficients of this series are called the triangular numbers.Using the formulas from the previous question, we can sum the infinite series: . 1+ 32 23 . 1 + 4 +... 32 . 2+ 2x 3 3 x4 4 x 5 + 3 32 33 22 23 . 1+ + .. . 22 Note: the Maple syntax for oo is infinity